Regular graphs are the graphs in which degree of each vertex is same. [Weisfeiler-Lehman Algorithm][1] fails to distinguish between given two non-isomorphic regular graphs. 

Is there a fastest known algorithm for regular graph isomorphism? Are regular graphs are the hardest instance for graph Isomorphism? Is there any combinatorial or algebraic to deal this situation efficiently?


  [1]: https://link.springer.com/chapter/10.1007/978-3-319-57586-5_22